Question

If repetition is allowed, then the total number of $4$-digit numbers that can be formed using the digits $1,2,5,6,7$ and that are divisible by $4,$ is

• A. $250$
• B. $150$
• C. $300$
• D. $125$

Answer 1

The correct option is B $150$

A number is divisible by $4,$ if the number formed by the last two digits is divisible by 4.
Last two digits can be filled in $6$ ways, i.e., $12,16,52,56,72,76$
Remaining $2$ places can be filled with $5$ digits in $5\times 5=25$ ways.
$\therefore$ Number of $4$-digit numbers divisible by $4$ is $6\times 25=150$